 If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.  The Elements of Geometry - Page 39by Webster Wells - 1894 - 378 pagesFull view - About this book
 | Webster Wells - Geometry - 1898 - 284 pages
...for GH its equal CH, we have BH+CH>BG, or BC>EF. PBOP. XXIX. THEOREM. 92. (Converse of Prop. XXVIII.) If two triangles have two sides of one equal respectively to two sides of the other, but the third side of the first greater than the third side of the second, the included angle of the first... | |
 | Henry W. Keigwin - Geometry - 1898 - 250 pages
...I. Restate ex. 3, page 23, using §§ 73 and 77a. 2. Restate § 76a. PROPOSITION XIII. THEOEEM. 78. If two triangles have two sides of one equal respectively to two sides of the other, hut the included angle of the first greater than the included angle of the second, then the a Y> Fio.... | |
 | Arthur A. Dodd, B. Thomas Chace - Geometry - 1898 - 468 pages
...hypotenuse and compare its area with the rectangle whose sides are the two legs of the right A242. If two triangles have two sides of one equal respectively to two sides of the other and the included angles supplementary, how are the areas related ? 243. The side of an equilateral... | |
 | Webster Wells - Geometry - 1898 - 250 pages
...altitude of an equilateral triangle is 3 ; find its area. 20. Two triangles are equivalent if they * have two sides of one equal respectively to two sides of the other, and the included angles supplementary. „ AD 21. One diagonal of a rhombus is five-thirds of the other,... | |
 | Webster Wells - Geometry - 1899 - 450 pages
...(Ax. 4) Substituting for GH its equal CH, we have PROP. XXIX. THEOREM. 92. (Converse of Prop. XXVIII.) If two triangles have two sides of one equal respectively to two sides of the other, but the third side of the first greater than the third side of the second, the included angle of the first... | |
 | Charles Austin Hobbs - Geometry, Plane - 1899 - 266 pages
...AAGH AH' A .45C = ABxAC ~?x ' A^Gff~^G£xAff' . A ABC = ABxAC (?, ' ADEF DE x DF' QBD 182 Ex. 538. If two triangles have two sides of one equal respectively to two sides of the other and the included angles supplementary, the triangles are equivalent. Ex. 539. Two triangles which have... | |
 | George Albert Wentworth - Geometry, Modern - 1899 - 272 pages
...side and the base produced. PROPOSITION XXVIII. THEOREM. 154. If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater... | |
 | George Albert Wentworth - Geometry - 1899 - 496 pages
...produced. BOOK I. PLANE GEOMETRY. PROPOSITION XXVIII. THEOREM. 154. If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater... | |
 | William James Milne - Geometry, Modern - 1899 - 258 pages
...DB ; that is, AB > DB or DE. Therefore, etc. QED Proposition XXXT 130. Construct two triangles that have two sides of one equal respectively to two sides of the other, but the third sides unequal. How do the angles opposite the third sides compare in size? Theorem. If two sides... | |
 | William James Milne - Geometry - 1899 - 398 pages
...its equal DH, AH+ HB>DB; that is, AB > Dn or DE. Proposition XXXI 130. Construct two triangles that have two sides of one equal respectively to two sides of the other, but the third sides unequal. How do the angles opposite the third sides compare in size ? Theorem. If two sides... | |
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